(The Friday before thanksgiving break:) An example of a bad induction proof: P(n) = "In any set of n horses, all the horses are white" Dots-on-foreheads concluded (as induction). Cardinality (quickly): N &vs; 2N; N &vs; Z; N &vs; Σ*; N &vs; N×N; N &vs; Q; N &vs; R.